Branching quantifier

Abstract: This paper presents Dependency Tree Semantics (DTS), an underspecified logic for representing quantifier scope ambiguities. DTS features a direct interface with a Dependency grammar, an easy management of partial disambiguations and the ability to represent branching quantifier readings. This paper focuses on the syntax of DTS, while does not take into account the model-theoretic interpretation of its well-formed structures 1 .

Abstract: This paper presents a modified realizability interpretation of classical linear logic. The interpretation is based on work of de Paiva (1989), Blass (1995), and Shirahata (2006) on categorical models of classical linear logic using Godel's Dialectica interpretation. Whereas the Dialectica categories provide models of linear logic, our interpretation is presented as an endo-interpretation of proofs, which does not leave the realm of classical linear logic. The advantage is that we obtain stronger versions of the disjunction and existence properties, and new conservation results for certain choice principles. Of particular interest is the simple branching quantifier used in order to obtain a completeness result for the modified realizability interpretation.

Abstract: Dependency Tree Semantics (DTS) is a formalism that allows to underspecify quantifier scope ambiguities. This paper provides an introduction of DTS and highlights its linguistic and computational advantages. From a linguistics point of view, DTS is able to represent the so-called Branching Quantifier readings, i.e. those readings in which two or more quantifiers have to be evaluated in parallel. From a computational point of view, DTS features an easy syntax---semantics interface wrt a Dependency Grammar and allows for incremental disambiguations.